Multiscale contact mechanics model for RF-MEMS switches with quantified uncertainties

We introduce a multiscale model for contact mechanics between rough surfaces and apply it to characterize the force-displacement relationship for a metal-dielectric contact relevant for radio frequency micro-electromechanicl system (MEMS) switches. We propose a mesoscale model to describe the history-dependent force-displacement relationships in terms of the surface roughness, the long-range attractive interaction between the two surfaces, and the repulsive interaction between contacting asperities (including elastic and plastic deformation). The inputs to this model are the experimentally determined surface topography and the Hamaker constant as well as the mechanical response of individual asperities obtained from density functional theory calculations and large-scale molecular dynamics simulations. The model captures non-trivial processes including the hysteresis during loading and unloading due to plastic deformation, yet it is computationally efficient enough to enable extensive uncertainty quantification and sensitivity analysis. We quantify how uncertainties and variability in the input parameters, both experimental and theoretical, affect the force-displacement curves during approach and retraction. In addition, a sensitivity analysis quantifies the relative importance of the various input quantities for the prediction of force-displacement during contact closing and opening. The resulting force-displacement curves with quantified uncertainties can be directly used in device-level simulations of micro-switches and enable the incorporation of atomic and mesoscale phenomena in predictive device-scale simulations.